Scattering problem for Vlasov-type equations on the $d$-dimensional torus with Gevrey data
Fuente:
arXiv
Guardado en:
| Autores principales: | , , , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866914798931804160 |
|---|---|
| author | Benedetto, Dario Caglioti, Emanuele Gagnebin, Antoine Iacobelli, Mikaela Rossi, Stefano |
| author_facet | Benedetto, Dario Caglioti, Emanuele Gagnebin, Antoine Iacobelli, Mikaela Rossi, Stefano |
| contents | In this article, we consider Vlasov-type equations describing the evolution of single-species type plasmas, such as those composed of electrons (Vlasov-Poisson) or ions (screened Vlasov-Poisson/Vlasov-Poisson with massless electrons). We solve the final data problem on the torus $\mathbb{T}^d$, $d \geq 1$, by considering asymptotic states of regularity Gevrey-$\frac{1}γ$ with $γ>\frac13$, small perturbations of homogeneous equilibria satisfying the Penrose stability condition. This extends to the Gevrey perturbative case, and to higher dimension, the scattering result in analytic regularity obtained by E. Caglioti and C. Maffei in [14], and answers an open question raised by J. Bedrossian in arXiv:2211.13707. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_10182 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Scattering problem for Vlasov-type equations on the $d$-dimensional torus with Gevrey data Benedetto, Dario Caglioti, Emanuele Gagnebin, Antoine Iacobelli, Mikaela Rossi, Stefano Analysis of PDEs Mathematical Physics 35B40, 35Q83, 82D10 In this article, we consider Vlasov-type equations describing the evolution of single-species type plasmas, such as those composed of electrons (Vlasov-Poisson) or ions (screened Vlasov-Poisson/Vlasov-Poisson with massless electrons). We solve the final data problem on the torus $\mathbb{T}^d$, $d \geq 1$, by considering asymptotic states of regularity Gevrey-$\frac{1}γ$ with $γ>\frac13$, small perturbations of homogeneous equilibria satisfying the Penrose stability condition. This extends to the Gevrey perturbative case, and to higher dimension, the scattering result in analytic regularity obtained by E. Caglioti and C. Maffei in [14], and answers an open question raised by J. Bedrossian in arXiv:2211.13707. |
| title | Scattering problem for Vlasov-type equations on the $d$-dimensional torus with Gevrey data |
| topic | Analysis of PDEs Mathematical Physics 35B40, 35Q83, 82D10 |
| url | https://arxiv.org/abs/2405.10182 |